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The Opening of the New Thought
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Richard Wongkew
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PostPosted: Wed May 21, 2014 6:22 pm    Post subject: The Opening of the New Thought Reply with quote

Now we must have a splendid beginning. But we are still entangled by old works and danglings.

Yes, this is all deeply congenial. I have very strongly been encouraged to adopt the feeling that you have no sense about math in Plato, since you never say anything about it, except that others ‘don’t understand.’ But, one must not be too final in judgment, even the wise judge is often found to be unworthy, for the judge can not effectively judge the judge without great problem.

For the thoughtfulnes here spoken one must take quite seriously the scientific truth, truth as correctness, that is to be taken as wholly canonical. Ergo: technological dasein speaks of the Greeks, of Homer, and of the problem of being. This technological dasein claims only this one advantage, differing from the premises of all other ages, that herein it is known that all premises are historical, and wholly historical (Nietzsche and Kierkegaard for example did not quite get to that point, they were still, in the former case, anti- (ie stepchild-of-the-times), and in the latter case transcendent in the identity, as of the sage or knight of faith, thus still Christian or, by the logic of Hegel, one could say, thus still Chinese).

When Heidegger speaks of the ontological he doesn't name the phenomenological. The phenomenological names the way of being, and the way of proceeding in thinking, that doesn't draw distinction between psychic act and bodily act. The ontological names the way being is opened as across the different regimes of history or truth. Thus one can not speak of it simply by citing the phenomena of the Greek world as in the Homeric Iliad, it is the question of how that world is opened, or thought, but not what that world is.

We will then begin with Descartes, and show how math in Descartes differs from that of the math of Plato.

Thus, it is a species, and a great one, of the transformation of thought called Enlightenment, as the thought of mathamatical physics. Prior the opening of the object and subject there were several physics, half a dozen or so (eg, the Stoic, Epicurean, Aristotelian, Platonic, etc).

One can take no recipe to certainty into a world without math, the abyss of opinion means thus: one can not know, one is victim of induction, but one also can not not know, one is victim of primary premises which are inexplicable from our predicament.

Math in Plato offers then a refuge from experience, a sauntering and ruminating in the celestial spheres, but thought as from the immediate world, from the human being who straddles the earth and the heavens: thus, the being that is of the many things, ta panta, but open to the whole, hen.

In Descartes, we become extramundane in extremis. We leave the world. First it is asked, what is a world, and the answer is, that which can be held up to doubt. Descartes denies even the ground of Socrates, thus of the word, for he will not even say justice. Justice, or hospitality as Derrida calls it, has been much doubted, yet the old boring word is used, one can not have certainty about it, but one does know of it enough to say one is uncertain, thus the lie is put to Socrates the classical eiron.

Descartes says this, a power of unlimited force deceives me, so that I lay waste my powers, yet, I am such as to be deceived, so this much is certain. Then from that ground I may create, or produce a reality, through shapes, as with geometry, and then through the calculations of change, as through the new and sharp understanding as time-for, as calculative time in infinitesimal calculus.

Thus with Descartes the world is thought as an object in toto. A certain mathematical thing.

With this groundwork set we shall continue, in our next post, open to questions as always, and now from within the technological ground of modern life, thus the ground where all things are thought as susceptible of being brought to full-throttle. From within this being, we must then think the Greek things, thus we give up philology; we must not as the classicist bear this golden age within a doll, as a mere notional, only with sheer cyclops' hands can we clutch the former worlds, reins, and things passed and perhaps past. Our laboratory is in this way prepared for us.
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Richard Wongkew
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PostPosted: Wed May 21, 2014 7:02 pm    Post subject: Reply with quote

An instructive correction : ‘This technological dasein claims only this one advantage, differing from the premises of all other ages, that herein it is known that all premises are historical, and wholly historical’

‘all premises’ must be taken to mean, all hitherto. Since otherwise one should say too much, by asserting that they always shall be (historical).

This indicates also our primary way of working forward, by exhibiting and not by theorizing.
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Peter Blumsom



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PostPosted: Wed May 21, 2014 7:11 pm    Post subject: Reply with quote

Yes, regarding math in Plato, first of all please define your terms for this thread. What do you mean by 'math in Plato' - math as learning, or math as arithmetike or logistike? For the time being I will assume the second (though the first is always present).

I understand very clearly regarding one difference between Descartes, Vieta and Stevin. For Plato all begins with the monad, for the others it begins in zero. Try to understand the implications of this, philosophically I mean. For I am interested to see what you know about Plato thoughts on numbers.

This subject 'that I have no sense of in Plato' is a real boon to me because it means that perhaps you can clarify some of the points I still labour upon. I've asked many people questions but their answers are always disappointing due to their anachronistic assumptions.

Also we must not rush to the Europeans because there is a line to be traced (eventually) through Diophantus and the Alexandrians through the Arabs eventually arriving at Vieta. I have many questions concerning the development of this time-line. We proceed according to the slow perambulation of the Athenian Stranger in Laws.
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Richard Wongkew
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PostPosted: Thu May 22, 2014 11:02 pm    Post subject: Reply with quote

We can’t allow ourselves to be swallowed up by the dream of ancient worlds, the interchanges of the understanding of Plato point to the ones making the inquiry, listening to the texts talk, wherever they are brought from, we hear them today, and see them not transparently, but through manifest contemporaneity.

It is impractical to raise a lion cub in the house and suppose it will never become a danger to us. We can not thus trace a history, after the school of facticity, and then take the wild beast suddenly as a figure of historicist thought (only as an afterthought). Too much has flown into it, and influenced and dominated such a figure.

If we can hint towards a connection back in time from today to Plato’s time, there is a major set of changes inbetween, and we are stampeded over by history that happens between us and the moments in Plato.

On the other hand I would like to learn more about what Plato seems to say about number in relation to a whole. Does Plato find a connection between one library and the number one, in relation to the problem that a library may still be a whole library even when many or all books are removed from it, and other equipment as well. That is to say in relation to the primary ambiguity of the whole thing.

This question, I believe is obviated in our own time, for it is a figure of the accidental being, i.e., the Cartesian consciousness or the intellectual substance. This substance is thought as not existing, one calls it extramundane, subjective, illusion, it is properly nothing. This whole is not a qualia, but a kind of assertion of the true, according to Aristotle, the qualia is the hen (the departure from science).


The DNA, so to speak, is however useless if thought naively. For if we ask about the timeline we think already, by a blind presupposition, through the lens of modern thinking. History is unknown to former times, it is established as factual history only recently, but factually history is itself under radical attack. It lacks theoretical potency, yet it persists in practice as an entrenched and effete position (due perhaps to the situation of general confusion and the lack of a suitable replacement). In this, that is not a direct answer, I say only that one must presume to do the history already from today, and not as if starting in some other time.

not to ‘ rush to the Europeans’

Again, what you are asking us is valid, but at the same time we must remember in tracing this, we already are Western European in our Enlightenment objectivity, our technological thought.


Basic Considerations:

What is meager, though to outsiders it is too little, must be for the one who thinks the main thing, for one can not do more, insofar as one becomes secondary or tertiary and begins to point to evidence that is itself based on arbitrary premises, one believes a thicker or more real connection is there, as if by way of trust. We can not make up, or find, and then share in such a faith, as do the thoughtless. Yet, it is no faith to say, this is the most authoritative belief, i.e., about what the nature of things are, the modern belief.

Our workings-through, as a method, as it looks to us ourselves:

If exhibiting means showing publicly, what has gone before that there is the possibility of exhibiting?

Has something gone before in time, or in some other way?

What I find before me, the table, the cup of coffee, the people, the voices and the music, the aromas. Thus, ta panta, many kinds of things. These are not yet exhibited when I only see them there: they are not yet public.

They are spoken of and they become public, thus communication with another is the condition of the hen, the public thing.

Example: Wittgenstein says ‘death is not something in life’ thus it is only something that is publicly known, exhibited in newspapers and heard of from afar, there are ‘cases of death’, whereas my death is not an object of true inquiry. I can only ask about it, in the way I might ask an older person about earlier times, before I was born for instance.

The things we hear of publicly have this character of being often heard of, and of coming very close, but of never being mine. One can not quite touch the exhibited realm, yet it is undeniable.

The situation with ta panta is the reverse. I can truly inquire about the cup and the table and the voice of the ones who are there.

Is it that the many things come prior to their exhibiting, so that first I find them there and then I publicize them? How can that be if there are things, such as death, that we only know of publicly? It will make no sense to speak of observations that then become public, as public descriptions. Thus, we must give up all talk of time, and this is consistent with the Cartesian or modern view from which we speak not by theory, but simply by exhibited life, thus history as come to this time can not be understood as a moving forward in time.

What is said publicly, and exhibited, has come to this.

Exhibiting means for us primarily the speaking of the predicament of the human being (as one of the many kinds of things) this predicament does not come before its being spoken nor does it come after its being spoken.

Death as a premise of what people say about their predicament showed up one day, and prior to that it was not a bother, a background. This background, as of death that changes in its meaning or in the way it speaks, is something else, like a pivot, that belongs neither in the exhibited or the private. Our premise of the Cartesian or technological, as a timeless predicament, is like this too.

Human beings have no time.

When we as existentialists, i.e., historicists, (or as the confluence of several ages of thought) speak of time, since we then move away from what is believed, as of death, and ask, what do people say in the street, we talk in a strange way, and not quite truly. We do that not in order to learn more about the past, but for our own sake, because we do not have time (as if to go back in time, and then return). [it is meaningless here, at the outset, to speak, eg, of how we stand in relation to the terminology and thought of, say, diachronic and synthetic thought, etc]

In this we have been setting the groundwork for our investigation.

--

Here, one likely goes beyond simple exhibiting, so it is important to recover the cut back and simple exhibiting of what is, from what has been said too voluminously. And so to prize clear-eyed simplicity.
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Peter Blumsom



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PostPosted: Fri May 23, 2014 8:04 am    Post subject: Reply with quote

<<not to ‘ rush to the Europeans’

Again, what you are asking is valid, but at the same time we must remember in tracing this, we already are Western European in our Enlightenment objectivity, our technological thought.>>

Yes, it is true that we always look from our own vantage point, as individuals and cultures. Even in such an ‘objective’ study as numbers we have to be sure that we are not looking into mirrors of ourselves. Two things help: The genuine desire to hope that one’s own inner promptings are valid, that one is not motivated by the desire to write a book or gain credit in the eyes of those who surround us; and the belief that of all topics numbers are those which have a ‘technology’ or ‘self – episteme’ transcending mere culture. For instance, when we learn that the Pandavas were said to be five brothers all sons of the one Pandu, that ‘five’ and ‘one’ at least meant the same for the ancient writer of the Mahabharata as it does for us today, not withstanding a possible difference of base etc. If we can’t allow this, then we have no approach - but I think we can.

I already touched upon the problem of the monad and the zero with regard to Plato, but there are many others also. One that is hardly picked up on is that whereas, due to what started properly with the Greeks, we are set in the idea that maths always seeks the general in order to ascertain the particular, the ancient world (and the Greeks are partly ancient in this) were attracted greatly to the unique. This was prompted by a deep respect, at least in their case, for the ‘unbreakable monad’.

Let me explain, at least for readers, as you may already know what I insufficiently grasp at.

For example when it came to solutions to the Pythagorean triangle they were only interested in integer types. (Theaetetus’ solutions up to to 17, is well known.) And though Euclid gives a general solution he does not deal with numbers in the way that we conceive. That, of course, needs investigation.

I mentioned that, in the case of the zero and the monad, Plato had two ways of dealing with numbers. Logistike was more in the way we use numbers today, dealing with practical matters. However when we hear Socrates stating that the monad cannot be divided he refers to the ‘higher’ study of Arithmetike. We mustn’t fall prey to anachronism here. This study was more in line with what we might term ‘number theory’ though that title gives rise to all sorts of ghastly connotations. Anyway it has little to do with what we call arithmetic.

So Socrates was quite able to see an apple divided over and over even to a purée because it didn’t violate the monad itself, or the unit that made that apple ‘one’ apple. He could easily conceive that dividing would from the monadic view also be multiplying. But there is a genuine question as to what happens to the ‘form’. Is it possible to divide the idea of the apple as well as its matter? To answer that I suppose we may wonder whether it is possible to conceive of half an apple before we conceive of a whole apple. I believe that takes us part of the way of genuinely examining your genuine question

<<Does Plato find a connection between one library and the number one, in relation to the problem that a library may still be a whole library even when many or all books are removed from it, and other equipment as well. That is to say in relation to the primary ambiguity of the whole thing.>>

It is your question and you should best answer it. But I believe that it is not too great a thing for us to assume that both we today and Plato then would understand the question in a similar way. Where there would be a difference would concern the equipment with which the problem would be handled. This entails the examination of Plato’s technology, what was available, and how it was evolved along a sinuous line through the centuries, finally making contact with the Europeans in Vieta (I think). I admit it is an ambition that may be unattainable without the help of others who see the subject clearly.

When we look back hampered by our techne we need to carefully tease out what are the genuine questions (that interest man per se) and also the very primary arche or foundations the techne can summon to its aid and which must, in fact, exist in the questions themselves.

Heidegger in fact touches such concerns (according to his way, not Plato’s) in his commentary on the first three chapters of Metaphysics Theta. But unfortunately he didn’t think to develop these swift feints, though I think I know why.

I hope here you see my way of approach. It is a slow, cautious one waiting for any opening occuring meta hod. You will naturally approach it in your own way. I only hope we don’t end up like grasshoppers trying to find each other in the dark.
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Richard Wongkew
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PostPosted: Tue May 27, 2014 11:38 pm    Post subject: Reply with quote

I suppose we will have to go back to examples if we are to go on (since I am now giving a ragged diatribe that surely errs at many edges), but the examples are always set loose on this or that fixed way of thinking, polluted to the core.

But it strikes to me that of the sons of such a man who has five sons, we find that we speak in a commonsense language. Yet, with the Hindu during the age of these great epics, there was perhaps even no one who knew of probabilities, for instance. I take that, probability, as an example of the formal use of number. It plugs something from the world into a machinic mechanism. That is always the objection to logical formalism, it is only as good as its premises. Number had not yet suffered that unexpected descent at the moment, it remained unreadably ordinary, opaque & invisible.

Today we all know something of the use of probability, even those of us who have never heard of an ordinary distribution or of an outlier. The number is found to relate to the statistic, it is settled among our thoughts, and moreover to the demographic compilation of data, as gathered by this or that deliberatively calculative academic sage. The statistic is presented in this or that manner so as to be acclaimed or blamed according to the analysis of the data involved and the attitude of the ones receiving the information and so on.

Thus, I would say, the great danger is in assuming that although we can, in a way, understand what is said, that a man has five sons, we do so in something like the way we understand everything which is said to be objective.

If we would understand number, even in the way it is said in the street, five sons, we stand beside the crowd of many applications of number which thus threaten to dominate us from the start.

Thus, it could be said, the whole lofty science of phenomenology has this one end, to return to the simple saying, five sons, which goes no further into the division between the formal count, ready for logistic automation in the formula and statistical analysis, and the subjective, or person-in-the-street’s sense of what is said by ‘five’ sons.

We know what it means, it is intelligible, but it is also deeply polluted from the ancient point of view. A decay of the unalloyed understanding thus stands before us in the look of the five sons, in their average being there, as they stand before us.

“ If we can’t allow this, then we have no approach - but I think we can.”

One might approach but with the admission that the difficulty is real, thus that history is real. This is the meaning also of the element of the ‘Greek dasein’ or the ‘medieval Christian dasein.’ Which is to say that something that is not in this or that one of the sons who stands before me, who I count, nonetheless plays an invisible and determining role.

The approach must not move through time. Here, with this inquiry, we have no time. Time, with Aristotle, is the measurement of being, but being is always this being.

--

You always presuppose you know too much, that is perhaps a very British thing, thus the visibly nonsensical notion that the British are commonsensical -- sick British propaganda, of course! Generally the British mistake debate for philosophy, and philosophy for thoughtfulness. You yourself, do not exercise low debate, but you often revolve in your own inner paradise, at the expense of the concrete discourse.

‘It is your question and you should best answer it’

What am I take from that, except that you indeed know nothing of Plato’s understanding of numbers? Although, you have given an example about apples above, that you could have as well used to answer my question. very odd procedure, rather stupid. There is nothing subtle in playing the idiotic role of a sage, play acting at its lowest level.

Do you understand number in the Platonic thought as an idea? This the sense one has.

Heidegger does not take an idiosyncratic path as you intimate, or attempt to realize a particular personal way. Rather he does something that is very broadly related to the tradition, he starts, to use the broadest language, from the two eyes of man, the division between (history) inquiry and philosophy, then he moves to the philosophy of inquiry (thus the thinking of the transformations of experience itself). He calls that thinking.

Naturally that differs from Plato's method, for Plato is still learning to get hold of the concept, and Aristotle follows him in that, then the scholastics get firm hold of formal logic. One sees this all with far less silliness when one captures the look of the wider picture. Such collecting of monuments of peculiar character, as of Plato, read as a unique and vast mind, whilst undeniably real in a certain sense, is rather tedious tribute to the thoughtfulness which would better honour our predecessors.

This massively idiotic haute chic notion of ‘my own’ x or y, this or that thought, is merely the atomization of historicism (tufted with dumb Western pseudo-sagacity). One must have the Socrates of this or that time, since it is undoubtable that a man of a certain very high education living in nineteenth century Germany, for instance, will write a different history than a woman living in New York in the present day, but many of these transformations are highly suspect, they are mere froth, mousse. It is sheer idiocy so far as it does not stick to the primary and principal character of the thought, in its comprehensive difference from the thought of former times.

It is very boring to go on pretending this or that idiosyncratic character trait means original thought. One can see this more seriously treated in Dostoevsky, where originality has the primary meaning of what dominates, and so not what is merely different, as to say in some formal superficial or automated way, as is now the fad growing out of the collapse of philosophy, due to the fact that academics feel very guilty about continuing to do philosophy in America and England where science blared so brightly, thus they ran deeper into their hole than was by any means warranted.

At the same time the strongest thought dissipated and became the superficial study called sociology. Today there are no serious thinkers and the possibility of thoughtfulness is forgotten.

Where does Plato speak of number in the way you find enticing, offer us a way into the strange world with a quote?

So far I see in what you say a special concept, but yet one more concept under the good as thought by the early Greeks of the school of Plato.




---

in passing, an editorial comment on the 'global' situation

The extremis rebel fashion of personal philosophy, EGS philosophy for instance, in serious terms, offers nothing to the thoughtful. On the other hand, the oxbridge philosophy, externalism, musings of late logic, and such things, is simply the slow work of slow minds, long surpassed by the great thinkers of more than a hundred years ago.




--

How would Plato think the monad in relation to the hen, where the one, the hen, is thought as hen alongside ta panta, as the one and the many? thus I mean in the pre-Platonic fashion, as with Hericlitus, in the simplist division of the most-general thought from the particular look.

With Leibnitz the monad(s) is(are) thought as transcendental -- in its plethoric complex -- the thought of god. The monad is not experienceable, it is thought with Leibnitz as noumenal, it is in a way, not number. It is in a way the answer as to what motion is, the chief thing then becomes the answer about change, and the underpinnings of change. Thus it is the metaphysical underpinnings of infinitesimal calculus (as the belief about the nature of the world in its potent deepest stratum).

Here, it may be useful to remember that economics, was called first political arithmetic. And in relatively recent times. It seems what belongs more properly to the older thought is found here just as with the rubric natural history, which remained up until the twentieth century, as a name for inquiry into the animal world (but also geography, and in the widest sense, all the particulars).

Thus, as history (inquiry about the particulars) is set in place alongside philosophy (thought about what is general) the analysis of number may have a similar structure with the Greeks.

--

the jockeying of other thoughts,

If one with Plato names one son, then it speaks to the concept. The concept is not the reality. It is the idea. I.e., Socrates is the son of so and so, one son. The reality is of that man there, Socrates. The concept or idea refers to the man there. The magnitude as number then is a figure of the categories, thus a concept of the most general kind (highest genera). Whereas man only refers to this or that thing, magnitude refers to all things. It speaks to the predicament in which all things are thought, as the what to do there with being.

This is with scientific thinking is psychology, one speaks of subitizing. Thus of an innate rationality.

Would you say that you have noticed with Plato that the question of arithmetic is chiefly a matter of knowledge in regard to a trustworthy means of managing a society, as in the Laws? Plato treats with a mode of dealing with justice that does not have reference to the one there. Thus, it leads in extremis to objectivity. Because that is always seen as the very important possibility of unalloyed knowledge, the true light.
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Peter Blumsom



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PostPosted: Thu May 29, 2014 3:33 pm    Post subject: Reply with quote

You say:

<<If we would understand number, even in the way it is said in the street, five sons, we stand beside the crowd of many applications of number which thus threaten to dominate us from the start.>>

Well, we cannot know if the author meant the five to be a number that represents something else than just a quantity. That I’ll accept. Just as when Socrates opens the Timaeus with “One, two, three, where is the fourth?” he seems to be making a simple tally though the numbers have a peculiar resonance with later events in the dialogue. But I do believe that that a tally as a tally was as clear to a Greek as to us. If you do not agree I would ask you to give examples. If we are to discuss Plato and number, or any other topic, we need to go into detail, and that is something you have shown a general reluctance towards, preferring grandiose statement. I'd like to get away from that if possible, though if you find that impossible to comply with, I'll grin and bear it.

Regarding your library and its books, the reason I left it to you wasn't that I felt inadequate to answer. It's just that it doesn't seem to matter whether you give one answer or the other. The mind discerns whether it is a unity, or a multitude. If you took the books outside and dumped them on the street it would seem a multitude and no longer a library, though in fact it still could be. But it could be in Greek terms arithmos - a determinate unity of units. (Or perhaps a red herring - I cant see into your mind.)

The five sons of Pandu was meant to be just an example. There is nothing formal in what I said about them, just conversational. My great question is, are we able to be simple in addressing ourselves to these things? Doxa quickly assumes ‘naïve’ for simple and that I don’t mean. For example, I am going to say something simple. I read that the Greeks were not as tied to the number line as we moderns. That may or may not be true but two simple facts arise in the mind. Firstly if we have a basket of eggs we look at them and say – there are five eggs here. I am asked to count: one, two … etc. But the first egg I count is not really the first. In fact there is nothing ‘first’ about any of the eggs in the basket. So they don’t have allegiance to a number line. There is nothing particularly Greek about this, it probably has occurred to many of us because it has that disarmingly trivial character that can be applied to many ‘first steps’. Self-importance immediately discards them, for instance in this case we plonk the term 'cardinal' down on the table and kill further thought.

But the Greeks were particularly interested in these kind of things. Their arithmoi were grouped this way as duets, trios, quartets etc. In fact the Pythagorean tetractys was composed this way, in the form of triangular numbers. Triangular numbers are easy to sum. The fourth triangular number is ten but it is named after the four and not the ten. You mentioned the ghastly word subitizing; well it’s possible that the Pythagorean figurate-numbers were a form of that. It’s true that children who have not yet learnt to be ‘un-Greek’ respond to that way of counting, i.e. before they have become decimalized.

Connected is the Greeks tendency to geometrize rather than to arithmetize. In Meno Socrates demonstrates this to the lad he attempts to redeem from slavery. If you don’t know it well I suggest a slow read of the relevant passage.

Another thing that the Greeks were curious about were multipliers, which acted as kind of adverbial numbers – multiply by three etc. If we were to multiply our basket of 5 eggs by three – that is, three baskets of eggs, we notice that we do not multiply by three eggs as we would do in the case of adding eggs together. What I mean is you cannot add three to five eggs, but you can add three eggs to five eggs. On the other hand, if you multiplied 5 eggs by 3 eggs you would have 15 eggs squared, and square eggs wouldn’t fit in your eggcup.

So from this absurdity we learn that multiplication is a special case of addition, where the terms added are equal. And so it turns out that one of the numbers is not a concrete quantity (multiplicand) but an adverbial, and of a completely different character to the other. It is also true that either number can be multiplier or multiplicand (the concrete quantity) but not in the way I have visualised them above.

This follows in the mode of Greek thought: when they say “equal an equal number of times” (ison isakis) (Theaetetus 147e).

Multiplication is seen as better technology than adding when the circumstances are right and these adverbials have a special dunamis especially in such cases when the equality is folded in upon itself - and they call it to the power of two or whatever.

You may be interested to know that the Egyptians never multiplied, they always added but took advantage of that unique character of two: that when added to itself it is no more nor less than when multiplied by itself. It is the only number that has this character, making it unique application rather than general.

This Egyptian method was still used in medieval times under the name duplatio exploiting that unique character of twoness. None of this would have been boring to Plato whereas the agitated modern mind finds it difficult to rest on such simplicity having become 'adult' long before its time, due to the ridiculous cramming systems of modern education – a deep, deep concentration of nothing-in-particular.

You will note how completely in contrast is this approach to Platonic number than what you discuss here:

<<Which is to say that something that is not in this or that one of the sons who stands before me, who I count, nonetheless plays an invisible and determining role.>>

Although I can imagine Heidegger nodding sagely at the sound of the way you express yourself here, I believe a Greek might well be mystified.

It misses the whole essence of playfulness in their approach, replacing it with a kind of po-faced mask of Germanic cod-profundity.

Anyway, these kinds of characteristics I have highlighted are a moving away from the counted thing towards the numbers that count. Or rather, they don’t actually move away, they inhabit a realm betwixt and between. When Socrates makes his three repeated assertions at Republic about arithmetic (not logistic) being a subject that can lead the mind onwards to "the vision of reality" (521d;523d;524e) he cannot mean just poodling around in these aforesaid curiosities but the striking up of a decisive pathway from them towards a higher determination of what is already indicated in them and other such.

The first step isn’t actually about number itself but focuses upon the faculty under which stewardship numbers ‘play’ – that of dianoia. He wants to demonstrate, again in a disarmingly trivial example, the invisible demarcation between sense and thought, and in doing so, make visible an as yet unseen path which “draws the mind upwards and forces it to argue about the numbers themselves.”

I want to break off here so that you can comment on whether you want to perambulate with me along this path or whether you think it worthless, and would rather tackle the whole subject of Platonic number in your own way - because you have already said several times that I know nothing of Platonic number. Either option suits me as I am interested in any light that can be shown by anyone on these matters about which I frankly admit I am still learning.


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Peter Blumsom



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PostPosted: Sun Jun 01, 2014 8:32 am    Post subject: Reply with quote

I shall continue to pick up the points you make though I admit that my Pythagorean Platonizing is showing through.

<<If one with Plato names one son, then it speaks to the concept. The concept is not the reality.>>

Do you mean by ‘it’ the naming? But I think that this needn’t be a concept. Uttering the name for ‘one’ - do you think that is creating a concept? I see this as being what we could call ‘direct’. Plato is pointing out the son, nothing else. There is no intervening symbol. The concepts came in later when algebra was being conceived. The symbols stood for unity, a kind of abstract one, jostling for its existence with an all consuming zero, that no longer directly dealt with the universe; and so, in subtle thought, we (Western man) were suddenly in a universe that was not dealing directly with itself. The implications of this are not invisible.

But Pandu’s sons are determinedly numbered as 5. Later, what the Greeks picked up on was that even in such a simple tally there are certain unforeseen and unknown consequences, such as the assumption that there must be something underlying the counted object that even primitive man ‘understood’ without understanding. Pandu's sons, five in number, were not identical. Bhima was a giant of a man, and yet in the simple tally he is simply one-of-five. To the discerning Greeks this disengaged the counted object from the counting unit, something that the primitive farmer would not have even conceived of or even thought interesting. If we had been able to ask Ugh, when he took stock of his animals, why he counted his largest Ox as equal to a chicken he might not be able to answer. Even if you told him that the Ox ate fifty times as much and weighed many hundreds of times as much he might have articulated that he only wanted to know how many animals he owned. The food they ate was another issue - a different kind of calculation (though, again, that would hardly have registered).

Something was missing, for even so Ugh might have stopped and thought about this, seeing as his brain was as large as ours. What was missing was someone to ask him that decisive question. In other words there was no leisured class - no scribes, Brahmins or philosophers who could see another world of speculation knitted into, beneath or even ‘above’ appearances. Such a leisured class invented/discovered the sixty base system in ancient Sumeria, and solved forever the problem of calibrating the incredibly complex weights and measures systems extant. Of course the sexagesimal system went on to far greater things.

My point is that things didn’t start with the Greeks. The baton was handed over to them, but a baton that was growing more potent with every exchange. There is no evidence that the brilliant Sumero-Babylonian speculators ever envisaged ‘separate’ units or indivisible monads, in the way the Greeks did; and although they had a fully-fledged geometrical ‘algebra’ there was little notion of proof in the Greek sense. And once the Greeks had this notion of a dianoetic unit there was a possibility of ascending their hypotheses towards a noetic and indivisible monad and finally to h’en.

This is part of the background from which we should begin our own speculations. I admit that it still could be argued that 'there is nothing here to show that I have the slightest understanding of what math meant to Plato' (isn't that how it goes?) but I argue that this is a slow perambulation and Athenian patience is required.
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Richard Wongkew
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PostPosted: Mon Jun 02, 2014 9:05 pm    Post subject: Reply with quote

This is the response to the second part of your reply. Since I have written it already I will post it. I will return after reflecting over the first part.

Quote:
Do you mean by ‘it’ the naming? But I think that this needn’t be a concept. Uttering the name for ‘one’ - do you think that is creating a concept? I see this as being what we could call ‘direct’. Plato is pointing out the son, nothing else. There is no intervening symbol.


By concept I mean the essence. Socrates, if he stands there, is no concept, but the real man. But thought as man, he is the concept: man. Man means, thus, what that thing there is. The ‘is’ is a concept, thus, because it is what is asserted, and it obtains only in speech. Aristotle says the true and the false are said (have to do simply with) of what is asserted (in speech).

Quote:
‘there must be something underlying the counted object’


Is that not the same as the thinking of each eidos with Plato, of sound for instance? I think this shows the thinking is of the concept of number, as beside that of, eg, sound (not just this or that sound, but sound itself).

Quote:
‘(though, again, that would hardly have registered’


And in the same way, features that are mother’s milk for us, did not register for Plato. Thus the strange need for deconstruction of history in the reading. The unfiltered reading is thoughtless, something is wrong with the reader who does not apply this attentive practical solution. One must, if you ask me, assume that something simply can not be engrossed, and that we are not in position to see the past, there is no past properly speaking.

--

Quote:
‘no scribes, Brahmins or philosophers’



But, again, I find the basis of this sharp division unfounded. As with Homer, Nestor (a man ‘strong in council’ or assembly), as with any community, the wise man, the shaman, and so on.

I find some power to this model you provide us, but it is at the same time rather artificial if you ask me. If one wanted to graft a Marxist thought into this thinking, a claim about the support of the bodily need of the Philosophers, one must come to many hard questions, and arrive at a great many insurmountable difficulties and sound refutations. However, on the other hand, the basic thought is theoretically not wholly misleading, though we risk subjecting ourselves to the derivative power of a formulaic thought.

This view does not belong to us by nature, but it takes some sweat, the labour theory, if you wish, of the ‘’right’ to thoughtfulness.

Quote:
‘finally to h’en.’


We should seek to learn, then, if there is a difference in this architectonic assent, and that of the assent to the Agathos (the Good). Some proficiency would be required, however, vaguely speaking, there seems to be an analogy there with this thematic ‘dianoetic’ assent.


--
Quote:
‘The symbols stood for unity, a kind of abstract one’


That is profoundly interesting for us. Does that not show the creation of the theoretical world, cf. Nietzsche: it is said of Socrates, here the wild beast (the young Socrates) becomes the theoretical man, the first theoretical man. The great break from the dionysian.

Is it not in seed form what Descartes thought as the world, thought back into the foundation of the construction of the world by the extramundane ego? With Plato things remained with contemplation, reflection in the recondite realm of death, of thought: which the living man was open to, but did not live in, as in the material [Living in the material. (Aufenthalt im Material.)].


--

Something further occurred to me, which I believe is decisive. One can not be thought with Plato as a measure in the sense it is with Newton and Kant.

E.g.: the concept with Kant means that the measured object is the same for whoverso may encounter it. So the same Starbucks to the remote-mountain-dweller, as to the man of the modern Metropol. The same in measure, in raw Cartesian terms, not in the concept as what it is for, but the same phenomenologically, the same in truth (correctness), but not in essence.

It can take us some time before we can understand this but it is crucial, there is a great error in finding that fundamentally these two ways of thinking number are of the same character.

Metra, metron: boundary, horizon (translated into more practical terms). Horizon is not the measure of a yardstick, bound is not the scientific distance.

However, one should have some closer look at the geometric proportion as it appears in Plato and Aristotle in contradistinction to the human measure in affairs of State and of Justice. In the dead thought of the Greeks, the complete language, a document, there are some problems of importance, however this question is perhaps not the most crucial for us, I mean the myopic focus on number with Plato.
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Richard Wongkew
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PostPosted: Mon Jun 02, 2014 10:34 pm    Post subject: Reply with quote

Quote:
My great question is, are we able to be simple in addressing ourselves to these things?


The view is this: In Aristotle, the philosopher of Heidegger and Brentano, the sense data is said to be most reliable when it is singular, of one sense. I see red, I hear a tweet. It is said to be less reliable when it is mixed, thus I see and perhaps hear, and touch and so on, movement. There is said to be also another sense, the one that is the subject of the question in the Timaeus that we have touched on, it is accidental sense (Aristotle says, the accident is almost a lie). I see Socrates the one who knew Diomatia of such and such a place, the one who speaks, under the Plane trees in the grove, and makes the ears of the young tingle, and so on. This last sense is truly in the world, but it is highly approximate and unreliable, yet, the school of Historicism, sees this as the foundation of all thought. It is the air we breath (the thematic break from the theoretical with Kant, which beckons all thinking people about the year 1900, after the afternoon’s parlor game of the Enlightenment breaks up with the discovery of the arbitrariness of the foundations of physics). The bright light of the obstinacy of gossip. One tries to cultivate a candid world, but always stands on this invisible, or all too visible flooring (the Hen, thought as the inauthentic, as justice, as hospitality, as heterogeneity or as the pathological).


Quote:
‘the ghastly word subitizing’


What occurred to me here, is that the terrible word rationality has the same status with science, but with the great thinkers we must think through science, and not merely around it. In the same way, can one can show that the rational is present in children, in the sense that for example, it is rational to get water from this side of the river, and not from the opposite bank, since it is more efficacious? Perhaps only someone playing the games of theoretical philosophy, everything the intellectual is mocked for, will devise reasons to stray from the most efficient track.

Quote:
‘Another thing that the Greeks were curious about were multipliers,’


It is very interesting to see that the Greeks insisted on thinking the multiplier, that which happens by rote with us. It is perhaps significant when shown in the light of the earlier logical machines, procedures for drawing inference, which never became formal with the Greeks. And remained tied to the question about the concept, the premise. It seems to me the great fact is that the emphasis is on the premise with the Greeks, and not on the machine to make deductive inference as with modern students of so-called logic.

Quote:
‘Although I can imagine Heidegger nodding sagely at the sound of the way you express yourself here, I believe a Greek might well be mystified.’


No, the thought of history is thought in a pedestrian fashion. For instance, one makes a division between animal and man, but does not notice it when one carries out an inquiry, say, into some field-mole. It is too much taken as a matter of course to be noticed, the student is not instructed about it, and it is highly reliable. The sum of such things makes the flooring, as I have mentioned above. The thought itself is to be understood in connection with the older thought of the great variety of doxa, with the difference that the highest thought, that of the communal understanding or belief about the nature of the world, undergoes a process of change towards the peak of history.

Your notion of German thought is a slander based on the conditions which split Oxbridge from the other universities around the time of the first war. It is true, there is a kind of remainder of scholastic heaviness in the thought, but that is as much a part of the Greek being handed off through latin, and thus the natural difficulties being treated as necessary. In Heidegger, however, there is only very simple, if you like, peasant thought, and the difficulty is wholly due to patent ignorance of the tradition.

Quote:
‘When Socrates makes his three repeated assertions at Republic about arithmetic (not logistic) being a subject that can lead the mind onwards to "the vision of reality" (521d;523d;524e)’


Maybe you can draw some passage from these sections with a sharp wit, so we may look at it here?
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Peter Blumsom



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Location: Wembley, London, UK

PostPosted: Mon Jun 09, 2014 8:34 am    Post subject: Reply with quote

<<I see Socrates the one who knew Diotima of such and such a place, the one who speaks, under the Plane trees in the grove, and makes the ears of the young tingle, and so on. This last sense is truly in the world, but it is highly approximate and unreliable, yet, the school of Historicism, sees this as the foundation of all thought. What is ‘truly in the world’ and in what way is it approximate?>>

I walk Barn Hill and my eye randomly picks out a patch of weeds that on inspection I see I am mistaken and it is κοσμος. How can Brentano, Aristotle, Heidegger or Derrida help me when it is vision so proximate? Both quale and qualified, true to themselves, are slandered by the ‘eye’.

<<Your notion of German thought is a slander based on the conditions which split Oxbridge from the other universities around the time of the first war.>>

Well then let’s forget this silly bickering, it is beneath us, or should be. Let them all be as they are.

<<Maybe you can draw some passage from these sections with a sharp wit, so we may look at it here?>>

It takes more than sharp wit I think, for one needs a certain kind of stamina or sophrosune to look into the eye of darkness that is Greek mathematics. Dianoia is willing to do the work but not at doxa’s whims, if you know what I mean. Also it would need diagrams and some are averse to that. The answer clearly is to begin another thread which can be dedicated to this kind of thing saving the rather quixotic nature of our present discourse from being overburdened with ‘pictures’. These are things to discuss.

The material here is in itself unproblematic in a way. We know what he is saying without having the slightest idea of why he is saying it or where he is trying to lead us. This seems to be the favoured dynamic of Plato.

A finger is a finger is a finger … and even if we count fingers this is no more than a tally. He is careful not to undermine our present view. And we are encouraged to note the distinction in three fingers between the adjectival three and the onamatic or noun-like 'fingers’ – the count and the counted. It is this distinction, this separation, that is to be explored and finally understood.

A thousand fingers will not increase our knowledge of ‘finger as finger’ and would not disturb the slumber of the mind. And yet in measure itself – something that at this point is uninvestigated – there may arise ambiguities better dealt with by wakefulness than drowsiness.

I admire the surreptitious entry, not merely of dianoia, which is trumpeted, but dianoia in its role as the principle faculty of psuche – soul. This is not to be found in our school maths books. Soul being for Plato that which intercedes between nous and the fairytale world of opposites the senses offer, itself working by the same principles as dianoia, through comparison and equality - types which mingle in the higher eidos that promotes all things just, eschewing all things lacking in the just.

This ‘psychological’ level (in the Ficinian sense) of number lays out for us a far greater and richer subject than Ugh counting his farmyard animals. Dianoia is not merely seen as a logical faculty but something involved in the equilibrium of soul itself, especially that of the individual soul. When equality is challenged or balance destroyed, he can be talking of both number and of soul. This analogue is crucial to getting to grips with number in Plato.

“If, then, each is one and both two, the very meaning of ‘two’ is that the soul will conceive them as distinct. For if they were not separable it would not have been thinking of two, but of one.” REPUBLIC 524B

This is, to be sure, a persistent thought for Socrates and it plagued Plato also and until the end of his life. After all two is both a plurality and a unity and the very heart of participation as a working concept.

After all Socrates is made to ask, on Plato’s behalf, when you add one to one that’s already there, is it the one added that becomes two or is it both that is two? (PHAEDO 97 ish). Then he becomes even more forensic: “When they were far apart each was one and there was no two at that point – but when they came closer this became a reason for their becoming to be two”

Ancillary information becomes decisive at his point. What is this ‘coming together’ if it is not calculation itself or logistike? He says it earlier when he mentions ‘added’. Is not calculation a ‘bringing together’ that forces the separate ‘ones’ to become koinen. Remember how he chides the hapless Hippias:

“Each of us is ‘one’, but that very thing that each of us is, both of us are not; for we are not one but two.” [GREATER HIPPIAS 301d]

But did the ‘ones’ then disappear, or become subsumed in the two? This cannot be for, if they did, the two would then itself become one. And was Socrates saying that there was no two up to that point? Does he mean that in the whole history of the cosmos only at that random moment when he brought the pebbles ‘together’ was two born? I doubt it. He is talking of logistike or the art of calculation; something akin to what we today might call the single unknown ‘x-to-be-calculated’ whose non existence is no more than a blank in the small boy’s math’s exercise book to the right of the equals sign. After completing his homework the small boy goes to his teacher and says – ‘Look, what is this ‘two’? - Have you seen it before?’ – ‘Yes, thousands of times.’ – ‘But how do you know it is the same two?’ - ‘There aren’t any others’ explains the teacher’ hoping the lunch bell will intervene and put an end to this worrying conversation.

I doubt if there is much wit here but I open the subject up for investigation by greater wits.

<<However, one should have some closer look at the geometric proportion as it appears in Plato and Aristotle in contradistinction to the human measure in affairs of State and of Justice.>>

This is an aim, but more needs to be uncovered.
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Richard Wongkew
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PostPosted: Tue Jun 10, 2014 6:48 pm    Post subject: Reply with quote

I will return to speak about this number issue, but I was shocked by your lack of engagement with this very important issue about perception with the Greeks. One should hope this spirit of superficiality can be abolished. However one must continue to attempt to find sufficient edification and clarity even without assistance.

Quote:
I walk Barn Hill and my eye randomly picks out a patch of weeds that on inspection I see I am mistaken and it is κοσμος. How can Brentano, Aristotle, Heidegger or Derrida help me when it is vision so proximate? Both quale and qualified, true to themselves, are slandered by the ‘eye’.


What does ‘help’ mean here? The point is a description (in this case about the way Aristotle explicitly, and so the Greek philosophers by extension, thought about perception).

The point here is a third way of seeing, neither the consciousness of the many things, nor the essence of them, but the being. For example, in modern terms, a cow is a object that can be treated by the sciences, and ,also, there is a way we know what to do with it (as we know what to do with the Starbucks or with words on the page [our pre-scene as essence) above that there is also that it is holy, the holiness of the cow shows what it is for the Hindu (as das Man, the historical people) over and above what is to be done with it or what it is for science. You wrote
Quote:
‘My great question is, are we able to be simple in addressing ourselves to these things?’


In seeing the transformation of the highest meanings, according to what one could call beauty or what you name in this context by cosmos, we come to the view of being as such, thus without time. Now I will say something about that:

In this thinking we have no time means the same as that we see from within. Being is thought as time. By analogy, that Hericlitus is said to be ‘not yet’ metaphysical means the same as that the inanimate is not yet living. Because we as living beings speak from within life, and see the other things from life, in terms of life.

To say that Hericlitus is ‘no yet’ metaphysical is the same as to say that we have no access to Hericlitus. The question about the animal has this structure too, one simply can not speak of the animal in so far as one would speak of the animal as animal and not as, for example, the ‘not yet’ human. The important thing is the Aristotelian limit to controversy, that one does not try to say more than one might, to speak for the animal or the inanimate object, like those who simply deserve to be called fools do.

Thus, again, in passing an example in regard to an important matter of procedure, of how one proceeds in thinking, is this, Hegel says, simply, religion is no longer necessary with the modern state, whereas, by contrast, Weber attempts to treat the disenchantment of the world, in accord with the wave of Protestantism and the expulsion of the miracle.

One can see the difficult imbecilities that arise in the second case, and that whatever is lost in complexity in the first case is infinitely returned in clarity and in probity (one can honestly say what Hegel did, one might repeat that clearly and without blushing or blinking, even to a child, and with no saving clauses).

The pumpkinification of thought belongs also to the realm of the infinite proliferation of the saving clause, within the ground that is not marked out as the place of primary vagueness proper, but is not even located. Without the very simple location of the ambiguity, triviality is guaranteed.

If somthing is thought without time, it is thought without the human being, or the consciousness. This non-time thinking viewed epistemically is neither the empty set, which is filled out by the objects of science, nor the human time, thought as an unalloyed duration.
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Richard Wongkew
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PostPosted: Tue Jun 10, 2014 10:36 pm    Post subject: Reply with quote

It strikes me that properly one should not treat with a statement without understanding it. Here there is a chance that you have intended to say something:
Quote:
I walk Barn Hill and my eye randomly picks out a patch of weeds that on inspection I see I am mistaken and it is κοσμος.


‘I see I am mistaken and it is κοσμος.’ Is there something genuine said here? Do you mean the situation of aporia in the Timaeus or what? I am alarmed about the possibility of being misled by this example of yours.

Perhaps there is the stir of something interesting in these weeds, I am hoping you will come forward to show us.
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Peter Blumsom



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PostPosted: Wed Jun 11, 2014 12:14 am    Post subject: Reply with quote

Quote:
‘I see I am mistaken and it is κοσμος.’ Is there something genuine said here? Do you mean the situation of aporia in the Timaeus or what? I am alarmed about the possibility of being misled by this example of yours.


Will it be genuine if you approve or if I experienced it? (Have you any such?)

I could be talking of Timaeus because I think I know to what you refer – but I’m not. It was Phaedo

Why I plucked that unfolding from experience was because I could place it in my mind with this statement: Unless we can recognize Νους as a cause we cannot account for the διακοσμησις of the κοσμος – the ordering of the best possible order.
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Peter Blumsom



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PostPosted: Wed Jun 11, 2014 8:07 am    Post subject: Reply with quote

The best possible order is what the nous the craftsman has already ‘arranged’, before the glance, as a moving image of eternity; where ‘time’ ‘motion’ ‘image’ are all to be studied in a kind of separation though they are all seen complete together (no matter how sly the glance). It isn’t so much as nous is everywhere, more that everywhere is nous.

If Socrates had received this from the tradition, from Diotima - hierophant of Demeter - or even Anaxagoras, he wouldn’t have needed the second best ‘sailing’ of ‘discourse about eidei’. It was this missing account – the logos linking nous to the forms - that plagued Plato, with its numerical ghosting of the One and the many. Even Plotinus, who revered Plato, recognised this abyss.
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